Alginate extracted from widely cultured brown seaweed can be hydrolyzed by alginate lyase to produce alginate oligosaccharides (AOS) with intriguing biological activities. Herein, a novel alginate lyase Aly1281 was cloned from marine bacterium Pseudoalteromonas carrageenovora ASY5 isolated from mangrove soil and found to belong to polysaccharide lyase family 7. Aly1281 exhibited maximum activity at pH 8.0 and 50 °C and have broad substrate specificity for polyguluronate and polymannuronate. Compared with other alginate lyases, Aly1281 exhibited high degradation specificity and mainly produced di-alginate oligosaccharides which displayed good antioxidant function to reduce ferric and scavenge radicals such as hydroxyl, ABTS+ and DPPH. Moreover, the catalytic activity and kinetic performance of Aly1281 were highly improved with the addition of salt, demonstrating a salt-activation property. A putative conformational structural feature of Aly1281 was found by MD simulation analysis for understanding the salt-activation effect.